The Volunteer's Dilemma describes a situation where each player can either volunteer or defect. If at least one player volunteers, all other players marginally benefit from defecting. If no player volunteers, all players have a very low payoff. Generate a Volunteer' s Dilemma game with 4 players:

Confirm that a strategy is optimal if exactly one player volunteers:

The Discoordination game is a hybrid form of coordination and anti-coordination games, where one player's incentive is to coordinate while the other player tries to avoid this. Generate a Discoordination game with a volunteer and a detractor:

Find if a strategy of coordinated actions is Pareto efficient:

The Cournot Oligopoly game describes a situation where a group of firms produces the same good. Each firm must consider the production cost and the quantity the other firms are producing. Only the firms with the lowest price sell goods. Generate a Cournot Oligopoly game:

Find if the strategy where all players choose the second action is Pareto efficient:

This is intuitive when considering that, for all players, the payoffs are largest for the second action:

The Colonel Blotto game describes a situation where officers (players) are tasked to simultaneously distribute limited resources over several objects (battlefields). The player devoting the most resources to a battlefield wins that battlefield, and the gain (or payoff) is equal to the total number of battlefields won. Generate a Colonel Blotto game:

Find if the strategy of spreading the resources is Pareto efficient:

This is intuitive considering the second player has more resources, thus, spreading the resources increases the number of battlefields where the player can win:

Rock Paper Scissors is a zero-sum game, where either one player wins and the other loses, or there is a tie. Determine if the equiprobable strategy is Pareto efficient:

Consider the difference between pure coordination and dangerous coordination games. Similar to Rock Paper Scissors, determine if the equiprobable strategy is Pareto efficient in the pure coordination game:

For symmetric games, the equiprobable strategy is often worth testing. Asymmetrical games are rarely Pareto efficient with this strategy. Determine if the equiprobable strategy is Pareto efficient in the dangerous coordination game: